The prisoners’ problem, introduced by Simmons in 1983, describes how two individuals attempt to communicate covertly by exploiting subliminal channels without alerting a ”warden” who controls the communication. Via subliminal channels it is possible to transmit covert messages by embedding them into cryptographic digital data (traditionally by exploiting randomness that is used in probabilistic...

In this paper we are studying the relations between generated and accepted hyperedge replacement languages. In context freeness of hyperedge replacement grammars we can transform each grammar into an equivalent one in Greibach Normal Form (HRGNF). In order to create a pushdown automata for hyperedge replacement languages (PDAH) we build an algorithm to transform the planar structure of a hyperg...

A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asym...

We obtain a number of results regarding freeness, quasiconvexity and separability for subgroups of Coxeter groups, Artin groups and one-relator groups with torsion.

We establish the freeness of certain anticyclotomic Selmer groups of modular forms. The freeness of these Selmer groups plays a key role in the Euler system arguments introduced in [BD05]. In particular, our result fills some implicit gaps in [PW11] and [CH15] which in turn allows the results of these papers to hold for modular forms whose residual representations are not minimally ramified. Re...

Voiculescu’s asymptotic freeness result for random matrices is improved to the sense of almost everywhere convergence. The asymptotic freeness almost everywhere is first shown for standard unitary matrices based on the computation of multiple moments of their entries, and then it is shown for rather general unitarily invariant selfadjoint random matrices (in particular, standard selfadjoint Gau...

Given a quartic Galois extension $L/\mathbb{Q}$ of number fields and Hopf-Galois structure $H$ on $L/\mathbb{Q}$, we study the freeness ring integers $\mathcal{O}_L$ as module over associated order $\mathfrak{A}_H$ in $H$. For classical $H_c$, know by Leopoldt's theorem that is $\mathfrak{A}_{H_c}$-free. If cyclic, it admits unique non-classical structure, whereas if biquadratic, three such str...